Transport through macropores

Adsoiptive molecules transport through macropores to the mesopores and finally enter the micropores. The micropores usually constitute the largest portion of the internal surface and contribute the most to the total pore volume. The attractive forces are stronger and the pores are filled at low relative pressures in the microporosity, and therefore, most of the adsorption of gaseous adsoiptives occurs within that region. Thus, the total pore volume and the pore size distribution determine the adsorption capacity. 

For a macroporous sorbent the situation is slightly more complex. A differential balance on a shell element, assuming diffusivity transport through the macropores with rapid adsorption at the surface (or in the micropores), yields... 

Eor pesticides to leach to groundwater, it may be necessary for preferential flow through macropores to dominate the sorption processes that control pesticide leaching to groundwater. Several studies have demonstrated that large continuous macropores exist in soil and provide pathways for rapid movement of water solutes. Increased permeabiUty, percolation, and solute transport can result from increased porosity, especially in no-tiUage systems where pore stmcture is stiU intact at the soil surface (70). Plant roots are important in creation and stabilization of soil macropores (71). 

Compared with microporous and mesoporous materials, the larger, interconnected voids in macroporous materials potentially provide easier molecule transportation through the materials. This is of particular interest for the transport of large biomolecules (e.g., proteins and cells). The pore sizes in macroporous materials are usually from tens to hundreds of nanometers, and the pores are typically... 

Sorption/desorption is the key property for estimating the mobility of organic pollutants in solid phases. There is a real need to predict such mobility at different aqueous-solid phase interfaces. Solid phase sorption influences the extent of pollutant volatilization from the solid phase surface, its lateral or vertical transport, and biotic or abiotic processes (e.g., biodegradation, bioavailability, hydrolysis, and photolysis). For instance, transport through a soil phase includes several processes such as bulk flow, dispersive flow, diffusion through macropores, and molecular diffusion. The transport rate of an organic pollutant depends mainly on the partitioning between the vapor, liquid, and solid phase of an aqueous-solid phase system. 

Micropore mass transfer resistance of zeoUte crystals is quantified in units of time by r /Dc, where is the crystal radius and Dc is the intracrystalline diffusivity. In addition to micropore resistance, zeolitic catalysts may offer another type of resistance to mass transfer, that is resistance related to transport through the surface barrier at the outer layer of the zeoHte crystal. Finally, there is at least one additional resistance due to mass transfer, this time in mesopores and macropores Rp/Dp. Here Rp is the radius of the catalyst pellet and Dp is the effective mesopore and macropore diffusivity in the catalyst pellet [18]. 

To quantify such transport, the advection-dispersion equation, which requires a narrow pore-size distribution, often is used in a modified framework. Van Genuchten and Wierenga (1976) discuss a conceptualization of preferential solute transport throngh mobile and immobile regions. In this framework, contaminants advance mostly through macropores containing mobile water and diffuse into and out of relatively immobile water resident in micropores. The mobile-immobile model involves two coupled equations (in one-dimensional form) ... 

Macroporous membranes - these are membranes containing large pores. The pore size is usually between 0.1 and 1 pm. Convective transport through the pore space is the mechanism of diffusion in this case. 

In the case of macroporous membranes, the pores are of large enough size and the mechanism of diffusion is such that the diffusion coefficient of a solute through the membrane may be described as the diffusion coefficient through the solvent-filled pores of the membrane. The macroporous membrane may be characterized by a porosity, e, and a tortuosity, x, as well as a partition coefficient, Kp, which describes how the solute distributes itself in the membrane. These parameters are usually included in the description of transport in macroporous membranes by incorporating them into the diffusion coefficient as... 

The case of transport through microporous membranes is different from that of macroporous membranes in that the pore size approaches the size of the diffusing solute. Various theories have been proposed to account for this effect. As reviewed by Peppas and Meadows [141], the earliest treatment of transport in microporous membranes was given by Faxen in 1923. In this analysis, Faxen related a normalized diffusion coefficient to a parameter, X, which was the ratio of the solute radius to the pore radius... 

If zeolitic diffusion is sufficiently rapid so that the sorbate concentration through any particular crystal is essentially constant and in equilibrium with the macropore fluid just outside the crystal, the rate of mass transfer will be controlled by transport through the macropores of the pellet. Transport through the macropores may be assumed to occur by a diffusional process characterized by a constant pore diffusion coefficient Z)p. The relevant form of the diffusion equation, neglecting accumulation in the fluid phase within the macropores which is generally small in comparison with accumulation within the zeolite crystals, is... 

The transport properties across an MIP membrane are controlled by both a sieving effect due to the membrane pore structure and a selective absorption effect due to the imprinted cavities [199, 200]. Therefore, different selective transport mechanisms across MIP membranes could be distinguished according to the porous structure of the polymeric material. Meso- and microporous imprinted membranes facilitate template transport through the membrane, in that preferential absorption of the template promotes its diffusion, whereas macroporous membranes act rather as membrane absorbers, in which selective template binding causes a diffusion delay. As a consequence, the separation performance depends not only on the efficiency of molecular recognition but also on the membrane morphology, especially on the barrier pore size and the thickness of the membrane. 

Considering the microstructure of membranes, they can be categorized as porous, which allow transport through their pores, or dense, which permit transport through the bulk of the material [19]. Porous membranes are classified as microporous, mesoporous, and macroporous (see Section 6.2). 

The boundary condition of zero accumulation on the interface between macropores and solid phase is imposed. The effective diffusivity of the porous sample G1 with bimodal pore size distribution is summarized in Fig. 16, where the sample macro-porosity macro is varied on the horizontal axis. This effective diffusivity is compared with a situation where the diffusion transport in nanopores is omitted. The contribution of the transport through the nano-porous solid phase to the total diffusion flux is significant. The calculated effective... 

In the domain where the entity that is transported through a membrane is immiscible or not completely soluble in the contacting (exit) phase, such as the case of gas phase air or oxygen in water, the interfacial factor becomes overwhelmingly important over the transport characteristics of the bulk membrane phase, which is empty space. It is important to recognize that the surface of macroporous membrane consists of the solid phase and the gas phase (in the pore diameter exposed to the interface), and the interfacial aspect of the solid surface dominates the behavior of the gas phase that expands out of the pore. 

In all but extreme climates, the upper portion of the soil profile is extensively occupied by plant roots, which remove both water and mineral nutrients. Plants and other biota (such as insects and small mammals) create extensive networks of voids often referred to as macropores, which result in a heterogeneous, biporous (i.e., there are two porosity values, for micro- and macropores), and structurally very complex material. Macropores (and pipes, which are larger, continuous macropores) can play a significant role in water transport, although the exact role of flow through macropores versus flow through the rest of the soil matrix is not completely understood. For an overview of the types and mechanisms of formation of macropores, the reader is referred to Beven and Germann (1982). 

For porous membranes the mass transport mechanisms that prevail depend mainly on the membrane s mean pore size [1.1, 1.3], and the size and type of the diffusing molecules. For mesoporous and macroporous membranes molecular and Knudsen diffusion, and convective flow are the prevailing means of transport [1.15, 1.16]. The description of transport in such membranes has either utilized a Fickian description of diffusion [1.16] or more elaborate Dusty Gas Model (DGM) approaches [1.17]. For microporous membranes the interaction between the diffusing molecules and the membrane pore surface is of great importance to determine the transport characteristics. The description of transport through such membranes has either utilized the Stefan-Maxwell formulation [1.18, 1.19, 1.20] or more involved molecular dynamics simulation techniques [1.21]. 

The consideration of thermal effects and non-isothermal conditions is particularly important for reactions for which mass transport through the membrane is activated and, therefore, depends strongly on temperature. This is, typically, the case for dense membranes like, for example, solid oxide membranes, where the molecular transport is due to ionic diffusion. A theoretical study of the partial oxidation of CH4 to synthesis gas in a membrane reactor utilizing a dense solid oxide membrane has been reported by Tsai et al. [5.22, 5.36]. These authors considered the catalytic membrane to consist of three layers a macroporous support layer and a dense perovskite film (Lai.xSrxCoi.yFeyOs.s) permeable only to oxygen on the top of which a porous catalytic layer is placed. To model such a reactor Tsai et al. [5.22, 5.36] developed a two-dimensional model considering the appropriate mass balance equations for the three membrane layers and the two reactor compartments. For the tubeside and shellside the equations were similar to equations (5.1) and... 

In the context of transport, the presence of macropores plays a particular role. Macropores are large pores, which form at the macroscopic level an obviously distinguished pore system from the soil matrix pore system. Macropores constitute sometimes a separate and/or continuous network in which particle velocities may deviate systematically from those in the soil matrix. As a result, the solutes released in the macropore network will be subjected to a preferential flow as compared to flow in the matrix system and will not completely mix with the total pore water volume at short time intervals. Preferential flow through macropores is considered here as a macroscopic process since concentrations in the macropores cannot easily be determined separately from the concentrations in the micropore system. 

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